Method and system for device-independent determination of coordinates of a point displayed by means of a microscope

ABSTRACT

A method for non-instrument-dependent determination of coordinates of a point imaged using a microscope includes determining, at object-related reference coordinates of at least one imaged reference point in a DICOM coordinate system, corresponding first instrument coordinates of the at least one imaged reference point in an instrument-dependent coordinate system. Using the object-related reference coordinates and the corresponding fast instrument coordinates, a transformation rule convening instrument-dependent coordinates into corresponding coordinates of the DICOM coordinate system is determined. Then, using the transformation rule, second instrument coordinates of an imaged point are converted into non-instrument-dependent coordinates of the DICOM coordinate system.

The present invention relates to a method and a system for thenon-instrument-dependent determination of the coordinates of a pointimaged using a microscope, and a calibration slide for use therefor.

BACKGROUND

Microscopes are frequently used for detecting small structures whichcannot be made out with the naked eye and for discovering characteristicfeatures in such structures. A fundamental use for microscopy incytology, histology and pathology is for reviewing a specimen andlooking for structures, cells or combinations of cells and the likewhich are of interest. If the sites of these structures are found on thespecimen, it is desirable to note them, for a variety of reasons. Forexample, the structure found has to be located again at a later stage bythe same or a different user for checking, for further inspection or forquality control. For this purpose, many microscopes have a unit fordetermining the coordinates of positions of a point in aninstrument-dependent system of coordinates. By electromechanicallydetermining these coordinates, it is possible to return to the locationdiscovered at a later stage.

As a rule, however, the coordinates are instrument-dependent, i.e. thecoordinates for this instrument can only be accurately reproduced if nochanges have been made to the adjustment of the microscope and notolerances were present. However, if for example the microscope stage istaken away for repair and reinstalled, it will give differentcoordinates for the same location on the specimen from those originallydetermined. Moreover, the coordinate systems of different microscopes,even of the same type, are not (exactly) the same.

SUMMARY OF THE INVENTION

There is a need to provide interoperability between any two microscopes,so that, for example, a second user can access, on his system, areas ona specimen which a first user has identified and stored.

The present invention provides a method and system according to theinvention for non-instrument-dependent determination of coordinates of apoint imaged using a microscope. The method according to the inventionenvisages that first of all, at given object-related referencecoordinates (X₁, Y₁, Z₁) of at least one reference point E₁ in a DICOMcoordinate system, the relevant instrument coordinates (x₁, y₁, z₁) ofthe minimum of one imaged reference point E₁ in an instrument-dependentcoordinate system are determined and from them a transformation rule Φfor converting instrument-dependent coordinates (x, y, z) into thecoordinates (X, Y, Z) of the DICOM coordinate system is obtained. Then,for non-instrument-dependent coordinate determination, the instrumentcoordinates (x_(p), y_(p), z_(p)) of an imaged point P are converted bymeans of the transformation rule Φ discovered intonon-instrument-dependent coordinates (X_(p), Y_(p), Z_(p)) of the DICOMcoordinate system.

The “Digital Imaging and Communications in Medicine” (DICOM) standardwas developed for formatting and exchanging images of medical equipmentand integrated in this equipment. DICOM is known, inter alia, in theUSA, Europe and Japan. On 2nd Jul. 1999 in Virginia, USA, in Supplement15, the DICOM Committee laid down a standard for images obtained withvisible light in endoscopy, microscopy and photography (Supplement 15:Visible Light Image for Endoscopy, Microscopy and Photography). With thepresent invention, this purely specimen-related and thereforenon-instrument-dependent DICOM coordinate system can be implemented onany microscope. The technical solution of the procedure according to theinvention comprises two steps. First of all, the microscope coordinatesystem is calibrated so as to obtain a transformation rule forconverting instrument-dependent coordinates intonon-instrument-dependent coordinates of the DICOM coordinate system.After this calibration step, the coordinates of any imaged point can betransformed using this transformation rule into non-instrument-dependentcoordinates of the DICOM coordinate system. These latter coordinates canthen be re-accessed at a later stage or by a different user, even on adifferent microscope, although obviously the other equipment mustcontain a calibration facility for the DICOM coordinate system.

For the calibration step, in a particularly advantageous embodiment, acalibration slide is used for setting reference coordinates of theminimum of one reference point E1. This calibration slide hascalibration crosses on it, marking the set reference points, inaccordance with the provisions of the DICOM standard.

In order to be able to give optimum consideration to all transformationsin question in the (x, y) plane, namely translation, rotation andscaling, mathematically at least 2.5 reference points or calibrationcrosses are needed on the calibration slide. Additional points may beneeded if calibration is also to be carried out in direction z.

As certain types of slides are used in microscopy, it is advantageous toproduce a corresponding calibration slide for each type of slide and touse it for the process according to the invention.

For calibration purposes, three calibration crosses corresponding toreference points E₁, E₂ and E₃, for example, are provided on acalibration slide. The (X, Y, Z) coordinates of these reference orcalibration points E₁ to E₃ are fixed. They relate to the zero point ofthe DICOM coordinate system, which may be located at an outer corner ofthe slide.

The calibration points E₁ to E_(n) (n≧1) are selected using themicroscope stage and the respective (x₁, y₁, z₁), . . . , (x_(n), y_(n),z_(n)) value is received and stored in the native, i.e.instrument-dependent coordinate system of the microscope used. For thecalibration points E₁ to E_(n) the (X, Y, Z) values in the DICOMcoordinate system and after measurement the (x, y, z) values in thenative coordinate system are known, so that a transformation rule can becalculated using standard methods for converting instrument-dependentcoordinates into the non-instrument-dependent coordinates of the DICOMcoordinate system.

The transformation method which comes to mind for the (x, y) coordinatesis that of the overdetermined affine transformation. For thetransformations of translation, rotation and scaling by a scaling factorwhich occur in one plane, mathematically at least 2.5, in practicetherefore at least 3, reference points (calibration crosses) are neededif all the above-mentioned calibration possibilities are to be takeninto account.

The Z zero point of the DICOM coordinate system is on the surface of theslide (without a glass cover). As the native Z coordinates are alsoincluded in the calibration described above, the z value can also beconverted into the DICOM coordinate system. In the Z calibration,essentially two cases can be distinguished.

If during calibration z values of the surface of the calibration slideincrease or decrease in one direction of the (X, Y) plane, theindication is that the calibration slide is not lying preciselyhorizontally but constitutes a skewed plane inclined in the Z direction.In this case, to increase the accuracy, Z calibration should also becarried out with an approach in the form of an inclined plane, asotherwise the accuracy of the (X, Y) calibration will be reduced. Inthis case, the deviation Δz can be measured along the gradient of theinclined plane by focussing on the surface of the slide and then the Zcalibration can be carried out, for which mathematically at least 1.5points are needed. For a Z calibration of this kind together with anoverdetermined affine transformation in the (X, Y) plane, therefore, atleast 4 points (2.5+1.5=4) are needed on the calibration slide.

If, on the other hand, it is established that the z coordinates of someselected reference points on the calibration slide differ from oneanother without having the form of an inclined plane, a simpletransformation rule would be an averaging process, whereby the averageis taken of the above-mentioned z coordinates of the reference pointsand this average value is defined as the zero point in the z direction.In other words, the average value calculated for the z coordinatescorresponds to the zero point in the DICOM coordinate system.

It is also conceivable for the two above-mentioned effects to occur incombination.

A calibration slide having at least one reference point with presetreference coordinates in a DICOM coordinate system is proposed for usein the method according to the invention. As already stated, calibrationcrosses are provided on this calibration slide, constituting thereference points for the method according to the invention. In the DICOMcoordinate system the zero point is located on one of the outer cornersof the rectangular calibration slide. It is particularly advantageous ifthe calibration slide corresponds in shape and size to a known type ofslide used in microscopy.

For interoperability it is essential that the calibration is carried outon the respective systems (microscopes) using the method according tothe invention. The use of identical calibration slides is most suitablefor this purpose.

As the system for non-instrument-dependent determination of coordinatesof a point to be imaged using a microscope which comprises a unit fordetermining instrument coordinates (x_(p), y_(p), z_(p)) of an imagedpoint P, the invention provides a computer unit which calculates, frominstrument coordinates (x₁, y₁, z₁) of at least one imaged referencepoint E₁ and associated predetermined object-related referencecoordinates (X₁, Y₁, Z₁) in a DICOM coordinate system, a transformationrule Φ for converting instrument-dependent coordinates into coordinatesof the DICOM coordinate system. The computer unit for calculating thetransformation rule may be integrated in the microscope or may be a partof a peripheral computer.

Using this system according to the invention, instrument-dependentcoordinates can be converted into non-instrument-dependent coordinatesof the DICOM coordinate system. For this, the transformation rule Φcalculated is applied to the coordinates (x_(p), y_(p), z_(p)) of animaged point P and the corresponding coordinates (X_(p), Y_(p), Z_(p))are calculated in the non-instrument-dependent DICOM coordinate system.In order to automate the method according to the invention forcalibrating and then calculating non-instrument-dependent coordinates asefficiently as possible, it is useful to implement this method using acomputer program which is started up and executed, in particular, on theabove-mentioned computer unit of the system according to the invention.The computer program may be stored on data carriers such as CD-ROMs,EEPROMs or in the form of flash memories, or can be downloaded into theworking memory through various computer networks, such as Intranet orInternet.

When this computer program is run, for example after a calibration slidewith a DICOM coordinate system has been placed on the microscope stage,the reference points applied in the form of calibration crosses aremeasured (automatically) in the instrument-dependent coordinate systemand the corresponding coordinates are determined. After preferably threeor more such reference points have been measured, the computer programbegins to calculate the transformation rule. Then a sample is examinedusing the microscope and the instrument coordinates of a point ofinterest are automatically converted into non-instrument-dependentcoordinates of the DICOM coordinate system by the computer program,using the transformation rule.

The computer program can control the entire procedure described, byinteraction with the user, or automatically execute particular parts ofthe method in the form of program modules.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention and its advantages will now be described in more detailwith reference to an exemplifying embodiment shown in the drawings.

In the drawings:

FIG. 1 shows a system according to the invention for thenon-instrument-dependent determination of coordinates of a point to beimaged with a microscope, in schematic representation;

FIG. 2 shows a calibration slide according to the invention and amicroscopic image with a schematically shown part of the unit fordetermining instrument coordinates for calculating the transformationrule Φ;

FIG. 3 shows an imaged point P in the instrument-dependent coordinatesystem and in the DICOM coordinate system.

DETAILED DESCRIPTION

FIG. 1 shows, in highly schematic form, a microscope 1 with objective 7for the enlarged imaging of structures carried on a slide 6. Thesestructures may be cells or collections of cells but may also beindustrial structures such as semiconductor structures. Accordingly, theapplications of microscopy extend from the medical field (cytology,histology, pathology) into the industrial field (e.g. wafer productionor nanotechnology). In these fields it is essential that any conspicuousfeatures or faults in the structures can be marked and retrieved at alater stage or by a different user.

Frequently, a computer unit 2 is connected to the microscope 1 or to amicroscope camera 11 in order to allow microscopic images to be furtherprocessed and saved. In the interests of simplicity it will be assumedhereinafter that the microscopic images 8 can be viewed on a monitor 10of the computer unit 2 and that at least part of the unit 4 fordetermining instrument coordinates (coordinates in the microscopicimage) is also present in the computer unit 2.

The slide 6 is often applied to a microscope stage 5 by vacuum suction,the microscope stage 5 generally being adjustable in itsthree-dimensional position.

The object structures can be examined using a one-shot or a scan.

The image data transmitted from the microscope 1 or from the microscopecamera 11 to the computer unit 2 are displayed, in this embodiment, onthe monitor 10 of the computer unit 2 in an instrument-dependentcoordinate system, while for example by clicking on a particular pointin the display image using a mouse 12 the corresponding coordinates ofthis point can be determined and displayed and saved in the microscopesystem.

In the present case the computer unit 2 has a computer program which isable to derive a transformation rule Φ from coordinates of one or moreimaged reference points and the associated known preset referencecoordinates, based on a DICOM coordinate system, on the slide 6, bymeans of which equipment-dependent coordinates can be converted intocoordinates of a DICOM coordinate system (an example of a computerprogram of this kind can be found at the end of this specification). Itis expedient to calibrate the system by using as the slide a calibrationslide 3 with at least one reference point in a DICOM coordinate system,in order to calculate the transformation rule using the reference pointor points imaged.

The non-equipment-dependent determination of coordinates of an imagedpoint which constitutes, for example, a fault, a conspicuous feature oran error, is enormously advantageous for reliably retrieving the point.It enables it to be reliably found in spite of tolerances in the same orsimilar instruments, e.g. during subsequent monitoring using the sameinstrument or an instrument of the same construction, but also duringlater examination on different equipment or in remote microscopy(telepathology or remote diagnosis or operations).

FIG. 2 shows a calibration slide 3 with DICOM (XY) coordinate system andthe associated microscopic image with instrument-dependent (xy)coordinate system. The transformation rule Φ provides the correlationbetween the two coordinate systems.

The calibration slide 3 according to the invention has six calibrationcrosses 9 in this embodiment, corresponding to points E₁ to E₆ in aDICOM coordinate system X, Y, Z, while the zero point is in the topleft-hand corner of the calibration slide 3. In the interests ofsimplicity the Z coordinates will not be considered in the followingdescription. Possible options for the Z calibration are mentioned abovein the present description. In order to calibrate the system shown inFIG. 1, first of all the calibration slide 3 is placed on the microscopestage 5 and a microscopic image 8 is produced by means of the microscope1 and the computer unit 2. The bottom half of FIG. 2 shows a microscopicimage 8 of this kind with an instrument-dependent coordinate system x,y, while the corresponding instrument coordinates (x₁, y₁) to (x₆, y₆)at the calibration crosses shown (E1 to E6) can be determined using aunit 4. It should be mentioned that not all six calibration crosses 9have to be used for the calibration, but fewer calibration crosses maybe sufficient depending on the degree of precision required. Asdescribed above, however, it is expedient to use three calibrationcrosses to derive a transformation rule by overdetermined affinetransformation.

The method of overdetermined affine transformation (cf. the example atthe end of this description) is known per se and will therefore not bedescribed in detail hereinafter. There are also other possible methodsknown to the skilled man for deriving the transformation rule Φ. Theunit 4 for determining instrument coordinates determines the coordinatesof a suitable number of imaged calibration crosses, i.e. thecorresponding reference points E₁, E₂, E₃ . . . , in the x, y coordinatesystem. The coordinates of the corresponding calibration crosses 9(reference points) on the calibration slide 3 in the DICOM XY coordinatesystem are prescribed. From these, the computer unit 2 or, moreaccurately, a corresponding computer program running on this computerunit 2, can calculate the transformation rule Φ for convertinginstrument-dependent coordinates (x, y) into the coordinates (X, Y) ofthe DICOM coordinate system.

It is useful if calibration slides which correspond to the current slideformats are produced, by means of which associated transformation rulesΦ can be calculated, as described above.

Using the transformation rule Φ discovered, the instrument coordinates(x_(p), y_(p)) of an imaged point P, as shown in FIG. 3, can now beconverted into non-instrument-dependent coordinates (X_(p), Y_(p)) ofthe DICOM coordinate system. The point P may for example represent aconspicuous feature in a cell structure or a fault in a semiconductorstructure. The coordinates of the point P are determined by means of theunit 4 for determining instrument coordinates and are converted usingthe known transformation rule Φ into non-instrument-dependentcoordinates of the DICOM coordinate system. For subsequent monitoring orre-examination, the non-instrument-dependent coordinates of the point Ptogether with the specimen are submitted for re-examination. The systemin which the re-examination is carried out must, of course, also have acalibration facility for the DICOM coordinate system. In particular,this system has to calculate the associated instrument-dependentcoordinates of the point P from the DICOM coordinates supplied for thepoint P using the inverse transformation rule Φ⁻¹ so that this point canbe accessed again in the microscopic image 8.

The following is an example of a computer program written in Cprogramming language, by means of which forward and backwardtransformation of the coordinates from a native microscope coordinatesystem and the DICOM coordinate can be carried out using theoverdetermined affine transformation method:

/*-----------------------------------------------------------------*/ //calculation for overdetermined affine transformation // forward andbackward calculation // coordinate systems are: // nativemicroscope-coordinate system, slide-dependent // microscope-independentDICOM coordinate system/*-----------------------------------------------------------------*/#include <stdio.h> /** Function PROTOTYPES **/ //given: nativemicroscope coordinates, calculate DICOM coordinates void CalculateDICOMCoordinates ( double x_Microscope, double y_microscope,double *pX_DICOM, double *pY_DICOM ); // given: DICOM coordinates,calculate native microscope coordinates void CalculateNativeMicroscopeCoordinates ( double X_DICOM, double Y_DICOM,double *px_Microscope, double *py_Microscope ); // calculate coordinatetransformation coefficients for forward and back transformation intCalcForwBackwTransCoefficients( int NoOfGaugingPoints, double*x_MicroscopeSystem, double *y_MicroscopeSystem, double *x_DICOMSystem,double *y_DICOMSystem ); // reset transformation coefficients to defaultvalues  void ResetTransformationCoefficients (void);  intCalculateTransformation(  double *a, double *b, double *c,  double *d,double *e, double *f,  int NoOfGaugingPoints,  double *x_Microscope,double *y_Microscope,  double *x_DICOM, double *y_DICOM );  /* staticvariables for coordinate transformation */ /* forward transformationcoefficients */ double aFwd = 1.0; double bFwd = 1.0; double cFwd = 0.0;double dFwd = 1.0; double eFwd = 1.0; double fFwd = 0.0; /* backwardtransformation coefficients */ double aBwd = 1.0; double bBwd = 1.0;double cBwd = 0.0; double dBwd = 1.0; double eBwd = 1.0; double fBwd =0.0; int main (void) { // coordinates of calibration points E1 to E6 inDICOM and native microscope system double aX_DICOM

= {3000., 3000., 3000., 17000., 17000., 17000.}; double aY_DICOM

= {10000., 30000., 50000, 10000., 30000., 50000.}; double ax_Microscope

= {41000., 43000.,45000., 181000., 183000., 185000.}; double ayMicroscope

= {29400., 309400., 489400., 126600., 306600., 486600.}; doublexMicTest, yMicTest; double XDICTest, YDICTest; int i; printf (“\n\n”);printf (“Affin Transformation From Native Microscope To DICOM CoordinateSystem\n”); printf(“=======================================================\n”); printf(“\n\n\n”); printf (“Coordinates of gauging points\n\n”); for (i=0;i<=5; ++i) { printf (“E%d: X-DICOM=%10.1f Y-DICOM=%10.1f x-Mic=%10.1f y-Mic=%10.1f\n”, i+1, aXDICOM [i], aY_DICOM [i], axjvlicroscope [i],ay_Microscope [i]); printf (“\n\n”); if (0 ==CalcForwBackwTransCoefflcients (6, ax_Microscope, ay_Microscope,aX_DICOM, aY_DICOM)){ printf (“computation failed\n”); return 0; }printf (“forward calculation coefficients\n”); printf(“------------------------------\n”); printf (“X-DICOM = %.4f * x-Mic +%4f * y-Mic + %.4f\n”, aFwd.bFwd.cFwd); printf (“Y-DICOM = %.4f *x-Mic + %.4f * y-Mic + %.4f\n\n\n”, dFwd,eFwd,fFwd); printf (“backwardcalculation coefficients\n”); printf(“-------------------------------\n\n”); printf (“x-Mic = %.4f *X-DICOM + %.4f * Y-DICOM + %.4f\n”, aBwd.bBwd.cBwd); printf (“y-Mic =%.4f * X-DICOM + %.4f * Y-DICOM + %.4f\n\n\n”, dBwd.eBwd.fBwd); printf(“Tests of calculation\n”); printf (“.........................\n\n”);printf (“Test1 using microscope coordinates of gauging point E4 asinput\n”); printf (“\n\n”); xMicTest = 181000.; yMicTest = 126600.;printf (“***input***: x Microscope =%10.1f y Microscope=%10.1f\n”,xMicTest, yMicTest); CalculateDICOMCoordinates (181000., 126600.,&XDICTest, &YDICTest); printf (“*** result ***: x DICOM =%10.1f y DICOM=%10.1f\n\n”, XDICTest YDICTest); printf (“End of test1 \n\n”); printf(“Test2 applying forward and backward transformation to test point\n”);printf (“\n\n”); xMicTest =100000.; yMicTest = 250000.; printf (“***input ***: x Microscope =%10.1f y Microscope=%10.1f\n”, xMicTest,yMicTest); printf (“forward transform\n”); CalculateDICOMCoordinates(xMicTest, yMicTest, &XDICTest, &YDICTest); printf (“*” result ***: xDICOM =%10.1f y DICOM =%10.1f\n”, XDICTest, YDICTest); printf (“backwardtransform\n”); xMicTest = 0.; yMicTest = 0.;CalculateNativeMicroscopeCoordinates(XDICTest,YDICTest, &xMicTest,&yMicTest); printf (“*** result “*: x Microscope =%10.1f y Microscope=%10.1f\n”, xMicTest, yMicTest); printf (“End of test2 \n\n”); return 0;} /*-----------------------------------------------------------*/ //forward transformation: calculate DICOM coordinates from // nativemicroscope coordinates/*-----------------------------------------------------------*/ voidCalculateDICOMCoordinates ( // input: x,y coordinates in the microscopesystem double x_Microscope, double y_Microscope, //output: X.Ycoordinates in the DICOM System double *pX_DICOM, double *PY_DICOM ) {*pX_DICOM = aFwd * x_Microscope + bFwd * y{circumflex over( )}Microscope + cFwd; *PY_DICOM = dFwd * x_Microscope + eFwd *yMicroscope + fFwd;/*-----------------------------------------------------------*/ // backtransformation: calculate native microscope-coordinates from DICOM //coordinates/*-----------------------------------------------------------*/ voidCalculateNativeMicroscopeCoordinates( // input: X.Y coordinates in theDICOM System double X_DICOM, double Y_DICOM, //output: x,y coordinatesin the microscope system double *px_Microscope, double *py_Microscope ){ *px_Microscope = aBwd * X_DICOM + bBwd * Y_DICOM + cBwd;*py_Microscope = dBwd * X_DICOM + eBwd * Y_DICOM + fBwd; }/*===================================================*/ intCalcForwBackwTransCoefflcients ( int NoOfGaugingPoints, double*x_MicroscopeSystem, double *y_MicroscopeSystem, double ′x_DICOMSystem,double *y_DICOMSystem/*===================================================*/ if(NoOfGaugingPoints<3) return 0; if (0 == CalculateTransformation(&aBwd,&bBwd,&cBwd,&dBwd,&eBwd,&fBwd, NoOfGaugingPoints,x_MicroscopeSystem, y_MicroscopeSystem, x_DICOMSystem, y_DICOMSystem))return 0; if (0 == CalculateTransformation(&aFwd,&bFwd,&cFwd,&dFwd,&eFwd,&fFwd, NoOfGaugingPoints, x_DICOMSystem,y_DICOMSystem, x_MicroscopeSystem, y_MicroscopeSystem)) return 0; return1; } /*===================================================*/ voidResetTransformationCoefficients (void)/*===================================================*/ /* resetcoefficients */ aFwd = 1.0; bFwd = 1.0; cFwd = 0.0; dFwd = 1.0; eFwd =1.0; fFwd = 0.0; aBwd = 1.0; bBwd = 1.0; cBwd = 0.0; dBwd = 1.0; eBwd =1.0; fBwd = 0.0; }/*===================================================*/ IntCalculateTransformation ( double *a, double *b, double *c, double *d,double *e, double *f, int NoOfGaugingPoints, double *x_Microscope,double *y_Microscope, double *x_DICOM, double *y_DICOM )/*===================================================*/ { int i; double*xDIC, *yDIC, *xMic, *yMic; double r1, r2, r3, r4, r5, r6, r7, r8;double r9, r10, r11, r12, r13, r14, r15; r1=r2⁼r3=r4=r5=r6=r7=r8=r13=r14=r15=0.0; xDIC = x_DICOM; yDIC = y_DICOM;xMic = x_Microscope; yMic = y_Microscope; for (i = 0; i <NoOfGaugingPoints; i++) { r1 += *xDIC; r2 += *yDIC; r3 += *xDIC * *xDIC;r4 += *yDIC * *yDIC; r5 += *xMic; r6 += *xDIC * *yDIC; r7 += *xMic **yDIC; r8 += *xDIC * *xMic++; r13 += *yMic; r14 += *yDIC++ * *yMic;r15+=*xDIC++ **yMic++; } /* accounting of coefficients a, b, c */ for(i=1; <=2; i++) { r9 = r3 * r4 * NoOfGaugingPoints + 2 * r1 * r2 *r6 −r1 * r1 * r4 − r2 * r2 * r3\ − r6 * r6 ′NoOfGaugingPoints; /*transformation is singular */ if (r9 == 0.0) return 0; if(i == 2) { /*accounting of coefficients d, e, f */ r5 = n13; r7 = n14; r8 = n15; }r10 = r8 *r4 * NoOfGaugingPoints + r6 * r2 *r5 +r1 * r7 * r2 −\ r1 *r4 * r5 − r8 * r2 * r2 − r6 * r7 * NoOfGaugingPoints; r11 = r3 *r7 *NoOfGaugingPoints + r8 * r2 *r1 +r1 * r6 * r5 − ri * ri * r7 − r3 *r2\ * r5 − r8 * r6 * NoOfGaugingPoints ; r12 = r3 *r4 * r5 + r6 * r7 *r1+r8 * r6 * r2 \ − r8 * r4 * ri − r5 * r6 * r6 − r3 * r7 * r2; r10 =r10/r9; r11 = r11/r9; r12/=r9; if(i==1 ) { *a = r10; *b = r11; *c = r12;} else { *d = r10; *e = r11; *f = r12; } } return 1; }/*==================== End (end of file)=====================*/

The following text shows a printout as generated by the above programwhen six calibration points E1 to E6 are preset and then two tests arecarried out. The first test (Test1) carries out a back-transformationinto the DICOM coordinate system for calibration point E4, whereas thesecond test (Test2) carries out forward and back transformation of agiven test point (P):

Affine Transformation from Native Microscope to DICOM Coordinate System

Coordinates of gauging pointsE1: X-DICOM=3000.0 Y-DICOM=10000.0 x-Mic=41000.0 y-Mic=129400.0E2: X-DICOM=3000.0 Y-DICOM=30000.0 x-Mic=43000.0 y-Mic=309400.0E3: X-DICOM^ 3000.0 Y-DICOM=50000.0 x-Mic=45000.0 y-Mic=489400.0E4: X-DICOM=17000.0 Y-DICOM=10000.0 x-Mic=181000.0 y-Mic=126600.0E5: X-DICOM=17000.0 Y-DICOM=30000.0 x-Mic=183000.0 y-Mic=306600.0E6: X-DICOM=17000.0 Y-DICOM=50000.0 x-Mic=185000.0 y-Mic=486600.0forward calculation coefficientsX-DICOM=0.1000*x-Mic+−0.0011*y-Mic+−955.3433Y-DICOM=0.0022*x-Mic+0.1111*y-Mic+−4465.6743backward calculation coefficientsx-Mic=10.0000*X-DICOM+0.1000*Y-DICOM+10000.0000y-Mic=−0.2000*X-DICOM+9.0000*Y-DICOM+40000.0000Tests of calculationTest1 using microscope coordinates of gauging point E4 as input

*** input ***: x Microscope = 181000.0 y Microscope= 126600.0 *** result***: x DICOM = 17000.0 y DICOM = 10000.0End of test1Test2 applying forward and backward transformation to test point

*** input ***: x Microscope = 100000.0 y Microscope= 250000.0 forwardtransform *** result ***: x DICOM = 8764.7 y DICOM = 23528.1backward transform***result***: x Microscope=100000.0 y Microscope=250000.0End of test2

The printout of the above text produced by the program is reproducedbelow in German (as far as possible) for ease of understanding:

Affine Transformation vom nativen Mikroskop-zum DICOM Koordinatensystem

Koordinaten der EichpunkteE1: X-DICOM=3000.0 Y-DICOM=10000.0 x-Mic=41000.0 y-Mic=129400.0E2: X-DICOM=3000.0 Y-DICOM=30000.0 x-Mic=43000.0 y-Mic=309400.0E3: X-DICOM=3000.0 Y-DICOM=50000.0 x-Mic=45000.0 y-Mic=489400.0E4: X-DICOM=17000.0 Y-DICOM=10000.0 x-Mic=181000.0 y-Mic=126600.0E5: X-DICOM=17000.0 Y-DICOM=30000.0 x-Mic=183000.0 y-Mic=306600.0E6: X-DICOM=17000.0 Y-DICOM=50000.0 x-Mic=185000.0 y-Mic=486600.0Berechnungskoeffizienten für HintransformationX-DICOM=0.1000*x-Mic+−0.0011*y-Mic+−955.3433Y-DICOM=0.0022*x-Mic+0.1111*y-Mic+−4465.6743Berechnungskoeffizienten für Rücktransformationx-Mic=10.0000*X-DICOM+0.1000*Y-DICOM+10000.0000y-Mic=−0.2000*X-DICOM+9.0000*Y-DICOM+40000.0000BerechnungstestsTest1 unter Verwendung der Mikroskopkoordinaten des Eichpunktes E4 alsEingabe***Eingabe***: x Microscope=181000.0 y Microscope=126600.0***Ergebnis***: x DICOM=17000.0 y DICOM=10000.0Ende des Test1Test2 mit Hin-und Rücktransformation des Testpunktes***Eingabe***: x Microscope=100000.0 y Microscope=250000.0Hintransformation***Ergebnis***: x DICOM =8764.7 y DICOM =23528.1 RücktransformtionErgebnis***: x Microscope=100000.0 y Microscope=250000.0Ende des Test2

LIST OF REFERENCE NUMERALS

1 Microscope

2 Computer unit

3 Calibration slide

4 Unit for determining instrument coordinates

5 Microscope stage

6 Slide

7 Objective

8 Microscopic image

9 Calibration crosses, points on slide

10 Monitor

11 Camera

12 (Computer) mouse

P Imaged point

Φ Transformation rule

X, Y, Z Coordinates in the DICOM coordinate system, referencecoordinates

x, y, z Coordinates in the microscope system, instrument coordinates

E₁, . . . , E₆ Calibration crosses, points, reference points

1. A method for non-instrument-dependent determination of coordinates ofa point imaged using a microscope, the method comprising: determining,at object-related reference coordinates of at least one imaged referencepoint in a Digital Imaging and Communications in Medicine coordinatesystem, corresponding first instrument coordinates of the at least oneimaged reference point in an instrument-dependent coordinate system;determining, using the object-related reference coordinates and thecorresponding first instrument coordinates, a transformation rule forconverting instrument-dependent coordinates into correspondingcoordinates of the Digital Imaging and Communications in Medicinecoordinate system; and then converting, using the transformation rule,second instrument coordinates of an imaged point intonon-instrument-dependent coordinates of the Digital Imaging andCommunications in Medicine coordinate system.
 2. The method as recitedin claim 1 further comprising presetting the reference coordinates usinga calibration slide.
 3. The method as recited in claim 2 wherein thecalibration slide corresponds to a first type of microscope slide. 4.The method as recited in claim 2 further comprising providing thecalibration slide based on a first type of microscope slide.
 5. Themethod as recited in claim 1 wherein the determining the transformationrule is performed using an overdetermined affine transformation.
 6. Themethod as recited in claim 1 wherein the determining the transformationrule is performed using an overdetermined affine transformation for x, ycoordinates of the instrument-dependent coordinates.
 7. The method asrecited in claim 1 wherein the determining the transformation rule isperformed using at least one of an averaging and an inclined planeapproach.
 8. The method as recited in claim 1 wherein the determiningthe transformation rule is performed using at least one of an averagingand an inclined plane approach for a z coordinate of theinstrument-dependent coordinates.
 9. A calibration slide comprising atleast one reference point with preset reference coordinates in a DigitalImaging and Communications in Medicine coordinate system, the presetreference coordinates being usable to determine corresponding firstinstrument coordinates of the at least one reference point when the atleast one reference point is imaged by a microscope so as to enable thedetermining of a transformation rule for converting instrument-dependentcoordinates into corresponding coordinates of the Digital Imaging andCommunications in Medicine coordinate system.
 10. The calibration slideas recited in claim 9 wherein the slide has a shape and a sizecorresponding to a type of microscope slide.
 11. A system fornon-instrument-dependent determination of coordinates of a point to beimaged using a microscope, the system comprising: acoordinate-determination unit configured to determine instrumentcoordinates of an imaged point; and a computer unit configured tocalculate, from first instrument coordinates of at least one imagedreference point and associated predetermined object-related referencecoordinates in a Digital Imaging and Communications in Medicinecoordinate system, a transformation rule for convertinginstrument-dependent coordinates into coordinates of the Digital Imagingand Communications in Medicine coordinate system.
 12. The system asrecited in claim 11 wherein the computer unit is configured tocalculate, from the instrument coordinates of the imaged point using thecalculated transformation rule, corresponding non-instrument-dependentcoordinates in the Digital Imaging and Communications in Medicinecoordinate system.
 13. A computer readable medium having stored thereoncomputer executable process steps operative to perform a method fornon-instrument-dependent determination of coordinates of a point imagedusing a microscope, the method comprising: determining, atobject-related reference coordinates of at least one imaged referencepoint in a Digital Imaging and Communications in Medicine coordinatesystem, corresponding first instrument coordinates of the at least oneimaged reference point in an instrument-dependent coordinate system;determining, using the object-related reference coordinates and thecorresponding first instrument coordinates, a transformation rule forconverting instrument-dependent coordinates into correspondingcoordinates of the Digital Imaging and Communications in Medicinecoordinate system; and then converting, using the transformation rule,second instrument coordinates of an imaged point intonon-instrument-dependent coordinates of the Digital Imaging andCommunications in Medicine coordinate system.
 14. The computer readablemedium as recited in claim 13 wherein the computer executable processsteps are executable by a computer unit of a system fornon-instrument-dependent determination of coordinates of a point to beimaged using a microscope, the system comprising the computer unit and acoordinate-determination unit configured to determine instrumentcoordinates of an imaged point, the computer unit being configured tocalculate, from first instrument coordinates of at least one imagedreference point and associated predetermined object-related referencecoordinates in a Digital Imaging and Communications in Medicinecoordinate system, a transformation rule for convertinginstrument-dependent coordinates into coordinates of the -DigitalImaging and Communications in Medicine coordinate system.